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Squeeze theorem or sandwich theorem Video Lecture | Mathematics (Maths) for JEE Main & Advanced
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FAQs on Squeeze theorem or sandwich theorem Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What is the Squeeze Theorem in calculus? |  |
Ans. The Squeeze Theorem, also known as the Sandwich Theorem, is a fundamental theorem in calculus that states if f(x) ≤ g(x) ≤ h(x) for all x in an interval except possibly at x = c, and the limits of f(x) and h(x) as x approaches c are both L, then the limit of g(x) as x approaches c is also L.
| 2. How is the Squeeze Theorem used in calculus problems? | |
Ans. The Squeeze Theorem is used to evaluate limits of functions that are difficult to directly evaluate by substitution or other methods. By bounding the function between two simpler functions whose limits are known, the Squeeze Theorem allows us to find the limit of the original function.
| 3. What are the conditions for applying the Squeeze Theorem? | |
Ans. The conditions for applying the Squeeze Theorem include ensuring that the function you are trying to find the limit for is squeezed between two other functions, the limits of which are known. Additionally, the functions must be defined in a neighborhood of the point you are evaluating the limit at.
| 4. Can the Squeeze Theorem be used to find the limit of trigonometric functions? | |
Ans. Yes, the Squeeze Theorem is commonly used to find the limit of trigonometric functions. By bounding the trigonometric function between simpler functions, the Squeeze Theorem can help in evaluating limits involving trigonometric functions.
| 5. Are there any common mistakes to avoid when applying the Squeeze Theorem? | |
Ans. One common mistake to avoid when applying the Squeeze Theorem is incorrectly identifying the bounding functions. It is important to ensure that the function you are trying to find the limit for is truly squeezed between the two bounding functions to correctly apply the theorem. Additionally, pay attention to the domain of the functions involved to avoid errors in evaluating the limits.
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Nov 21, 2024 Last updated |
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